Given Euler's formula $e^{jx}=\cos(x)+j\sin(x)$ ($j$ is the imaginary number), could I know how to write the following $f(x)$ as a finite sum of complex exponentials:
1)$$f(t)=1+\cos(t)+\sin(2t+90^{\circ})$$ 2)$$f(t)=\cos^2(2t)+\sin(3t)$$
I know that $cos(t)\cdot$length is basically the vector's $"x"$ value, and $sin(x)\cdot$length is basically the vector's $"y"$ value. So you can convert a polar expression into a rectangular expression. But how could I convert those $cos$ and $sin$ into the sum of complex exponentials? And is $1$ can be viewed as $e^{j\cdot0}$?
Thanks a lot.